An Etymological Dictionary of Astronomy and Astrophysics
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An extension of the → Einstein model accounting for → specific heats, based on the concept of → elastic waves in → crystals. In this model specific heat is given by: C_V = 9R[(4/x²)∫ y²/(e^y - 1)dy - x/(e^x - 1)], integrating from 0 to x, where R is the → gas constant, k is → Boltzmann's constant, x = hν_max/k, and y = hν/k. The parameter T_D = hν_max/k is the characteristic → Debye temperature of the crystal. At low temperatures the specific heat prediction by this model is in good agreement with observations (→ Debye law), in contrast to Einstein's model.

→ debye; → temperature.

A model for a → cometary nucleus proposed by Fred Whipple (1950-51), according to which the nucleus is a solid body (a few kilometers across) made up of various → ices (→ frozen water, → methane, → ammonia, → carbon dioxide, and → hydrogen cyanide) in which → dust is embedded. Dust particles are liberated when the ices vaporize as the → comet approaches the → Sun, and they get blown away by → solar radiation pressure, often forming impressive, gently curved → dust tails.

→ dirty; → ice; → ball; → model.

A model describing → dwarf novae and → Soft X-ray Transient (SXT)s. Accordingly, these objects are triggered by an → accretion disk instability due to an abrupt change in opacities (→ opacity) at → temperatures at which hydrogen is partially ionized. All versions of the DIM have this ingredient. They differ in assumptions about → viscosity, and about what happens at the inner and outer disk radii. Basically, during → quiescence, material accumulates in the accretion disk until a critical point is reached. The disk then becomes unstable and is dumped onto the → compact object, releasing a burst of → X-rays. However, the greater duration of SXT bursts (months) and the time interval between bursts (decades) cannot be accounted for by the standard disk instability model used for dwarf novae, and additional factors such as X-ray illumination and irradiation of the accretion disk are required for the model to match the observed properties of SXTs (J-P Lasota and J-M Hameury, 1995).

→ disk; → instability; → model.

A model of → dust grains conceived to describe the observed → interstellar extinction properties. It is characterized by the abundance of the different → chemical elements locked up in the dust, and by the → composition, → morphology, and → size distribution of its individual grains. For example, → MRN dust model.

→ dust; → model.

A theory for the generation of a star's or planet's magnetic field by the circulation of conducting fluids inside it. → solar dynamo.

→ dynamo; → model.

A model for the → specific heat of solids in which the specific heat is due to the vibrations of the atoms of the solids. The vibration energy is → quantized and the atoms have a single frequency, ν. Put forward in 1907 by Einstein, this model was the first application of → quantum theory to the solid state physics. The expression for the specific heat is given by: C_V = 3Rx²e^x/(e^x -1)², where R is the → gas constant, x = T_E/T, T_E = hν/k, h is → Planck's constant, and k is → Boltzmann's constant. T_E is called the → Einstein temperature. This model could explain the temperature behavior of specific heat but not very satisfactorily at low temperatures. It has therefore been superseded by the → Debye model. See also → Dulong-Petit law.

Albert Einstein in 1907; → model.

A model, based on theoretical calculations, which predicts the behavior of an astronomical entity (stars, galaxies, Universe) over time.

→ evolutionary; → model.

1) Geology: The process whereby a geologic section (subsurface model of one-, two-, or three dimensions) is transformed into a synthetic seismogram (synthetic seismic record).
2) In → asteroseismology, a model that takes the physical properties of a star as input parameters and predicts the star's oscillations. Then, by finding parameters that yield oscillation frequencies (ω_nlm) close to those observed, one can infer the properties of the observed star. The quantum numbers n, l, and m must be identified before any meaningful comparison between seismic data and model predictions can be made. That mode identification requires a physical interpretation of the measured frequencies.

→ forward; → seismic; → modeling.

A class of → Big Bang models of the Universe that include a finite period of accelerated expansion in their early histories. Such an event would have released enormous energy, stored until then in the vacuum of space-time. The horizon of the Universe expanded, temporarily, much faster than the speed of light. → inflaton field.

Inflationary, adj. of → inflation; → model.

The → standard model of → Big Bang that incorporates both → dark matter and → dark energy. See also → cold dark matter (CDM).

→ lambda, → cosmological constant; → cold; → dark; → matter; → model.

A stellar atmosphere model which includes metals or uses methods to reproduce their effects, → line blanketing.

→ line; → blanket; → model.

A → magnetohydrodynamic model devised to account for the → bipolar jets and → outflows observed around → protostars. Basically, a → poloidal magnetic field is frozen into a rotating → accretion disk. If the angle between the magnetic field lines threading the disk and the rotation axis of the disk is larger than 30°, the plasma can be accelerated out of the accretion disk along the field lines. The field lines rotate at a constant → angular velocity, and as the gas moves outward along the field lines, it is accelerated by an increasing → centrifugal force (magnetocentrifugal acceleration). At some point, when the rotation velocity is about the same as the → Alfven velocity in the gas, the field lines get increasingly wound up by the inertia of the attached gas and a strong → toroidal magnetic field component is generated. The toroidal component is the main agent in collimating the flow into a direction along the → open magnetic field lines. The earliest version of the model was proposed by Blandford & Payne (1982, MNRAS 199, 883). It has two main versions: → X-wind and → disk wind models. See also → magnetorotational instability.

→ magneto-; → centrifugal; → model.

Same as → Milne Universe.

→ Milne Universe; → cosmological; → model.

1a) A mathematical representation of a process, system, or object developed to understand its behavior or to make predictions. The representation always involves certain simplifications and assumptions. See also → theory, → hypothesis.
1b) A mental image of a phenomenon using familiar terms (or images). For example, in the Bohr model the atom is visualized as a nucleus with electrons orbiting around it in a manner similar to the way that planets revolve around the Sun. While this model is use ul in understanding the atom, it is an over-simplified description of a real atom and does not describe/predict all of its attributes (G. Smooth, Lawrence Berkeley Lab website).
2) To make or construct a model of.

M.Fr. modelle (Fr. modèle), from It. modello "a model, mold," from V.L. *modellus, from L. modulus "measure, standard," from modus "manner, measure" (cf. Av. mad-, → mode), PIE *med- + -ulus, → -ula.

1) Model, from Fr. modèle. Tarzâl, from tarz, → mode + -âl, → -al.
2) Model sâxtan, from model + sâxtan, sâzidan "to build, make, fashion; to adapt, adjust, be fit" (from Mid.Pers. sâxtan, sâz-, Manichean Parthian s'c'dn "to prepare, to form;" Av. sak- "to understand, to mark," sâcaya- (causative) "to teach").
Tarzâlidan, from tarzâl + -idan infinitive suffix.

In a theoretical analysis, the solution that does not correctly treat the intervening parameters, or neglects some crucial factors.

→ model. dependence, noun of → dependent.

The simulation of a process, concept, or operation of a system often implemented by a computer program and making use of a mathematical treatment.

Verbal noun of → model

A model concerned with the distribution in size of → interstellar grains to account for observations of → interstellar extinction from 0.11 μm to 1.0 μm. The → distribution has the form N(a)da ∝ a^-3.5da, where a is the grain radius. It extends from 5 nm to 1 μm for → graphite and over a narrower range for other materials.

MNR, the initials of authors J. S. Mathis, W. Rumpl, and K. H. Nordsiek (1977, ApJ 217, 425), who introduced the mode; → dust; → model.

The prediction of the evolution of a system via numerical construction of approximate solutions to the governing equations.

→ numerical; → modeling.

A stellar model in which the rotation axis is tilted relative to the magnetic dipole axis. As the star rotates, observable quantities (e.g. the line-of-sight component of the magnetic field, stellar brightness, emission lines) are modulated according to the rotational period. Such a model was first put forward by D. Stibbs (1950, MNRAS, 110, 395).

→ oblique; → rotator; → model.

A model of galaxy formation in which regions of primordial gas as massive as clusters of galaxies began to collapse into thin sheets (pancakes). Within the pancakes, smaller regions of gas later collapsed to form individual galaxies.

→ pancake; → model.